A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions have been given for more than fifty years to millions of students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone preparing for the Mathematical Olympiads will find many useful ideas here, but people generally interested in logical problem solving should also find the problems and their solutions stimulating. The book can be used either for self-study or as topic-oriented material and samples of problems for practice exams. Useful reading for anyone who enjoys solving mathematical problems, and equally valuable for educators or parents who have children with mathematical interest and ability.

The importance of mathematics competitions has been widely recognised for three reasons: they help to develop imaginative capacity and thinking skills whose value far transcends mathematics; they constitute the most effective way of discovering and nurturing mathematical talent; and they provide a means to combat the prevalent false image of mathematics held by high school students, as either a fearsomely difficult or a dull and uncreative subject. This book provides a comprehensive training resource for competitions from local and provincial to national Olympiad level, containing hundreds of diagrams, and graced by many light-hearted cartoons. It features a large collection of what mathematicians call "beautiful" problems - non-routine, provocative, fascinating, and challenging problems, often with elegant solutions. It features careful, systematic exposition of a selection of the most important topics encountered in mathematics competitions, assuming little prior knowledge. Geometry, trigonometry, mathematical induction, inequalities, Diophantine equations, number theory, sequences and series, the binomial theorem, and combinatorics - are all developed in a gentle but lively manner, liberally illustrated with examples, and consistently motivated by attractive "appetiser" problems, whose solution appears after the relevant theory has been expounded. Each chapter is presented as a "toolchest" of instruments designed for cracking the problems collected at the end of the chapter. Other topics, such as algebra, co-ordinate geometry, functional equations and probability, are introduced and elucidated in the posing and solving of the large collection of miscellaneous problems in the final toolchest. An unusual feature of this book is the attention paid throughout to the history of mathematics - the origins of the ideas, the terminology and some of the problems, and the celebration of mathematics as a multicultural, cooperative human achievement. As a bonus the aspiring "mathlete" may encounter, in the most enjoyable way possible, many of the topics that form the core of the standard school curriculum.

The Original Collection of Math Contests: Lessons and Problems for Elementary School, authored and edited by volunteers of the Orange County Math Circle, contains six topical lessons and two full years of OCMC's Thanksgiving Tournament for grades 3 through 6. With over 400 problems with full solutions, this book is a great resource for elementary schoolers looking to get started with competition math, sharpen their skills, or simply enjoy the process of learning.

Elementary School Math Contests contains over 500 challenging math contest problems and detailed step-by-step solutions in Number Theory, Algebra, Counting & Probability, and Geometry. The problems and solutions are accompanied with formulas, strategies, and tips.This book is written for beginning mathletes who are interested in learning advanced problem solving and critical thinking skills in preparation for elementary and middle school math competitions.

The Alberta High School Mathematics Competition was the first and oldest in Canada to be run on a provincial scale. It started in 1957 and its fifty years can be broken down to three periods : ancient (1957-1966), medieval (1967-1983) and modern (1984-2006), which reflect what was taught in the schools of the day. The first two periods are primarily of historical interest. During the modern period, the problem committee was led by the well-known problemist Murray Klamkin, and composed many innovative and challenging problems. This book contains all the problems and answers for the first fifty years of the competition, up to 2005 / 2006 and full solutions are provided to those from the modern period, often supplemented with multiple solutions or additional commentaries.

Any high school student preparing for the American Mathematics Competitions should get their hands on a copy of this book! A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions (AMC) have been given for more than fifty years to millions of high school students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone taking the AMC exams or helping students prepare for them will find many useful ideas here. But people generally interested in logical problem solving should also find the problems and their solutions interesting. This book will promote interest in mathematics by providing students with the tools to attack problems that occur on mathematical problem-solving exams, and specifically to level the playing field for those who do not have access to the enrichment programs that are common at the top academic high schools. The book can be used either for self-study or to give people who want to help students prepare for mathematics exams easy access to topic-oriented material and samples of problems based on that material. This is useful for teachers who want to hold special sessions for students, but it is equally valuable for parents who have children with mathematical interest and ability. As students' problem solving abilities improve, they will be able to comprehend more difficult concepts requiring greater mathematical ingenuity. They will be taking their first steps towards becoming math Olympians!

All too often, through common school mathematics, students find themselves excelling in school math classes by memorizing formulas, but not their applications or the motivation behind them. As a consequence, understanding derived in this manner is tragically based on little or no proof. This is why studying proofs is paramount! Proofs help us understand the nature of mathematics and show us the key to appreciating its elegance. But even getting past the concern of "why should this be true?" students often face the question of "when will I ever need this in life?" Proofs in Competition Math aims to remedy these issues at a wide range of levels, from the fundamentals of competition math all the way to the Olympiad level and beyond. Don't worry if you don't know all of the math in this book; there will be prerequisites for each skill level, giving you a better idea of your current strengths and weaknesses and allowing you to set realistic goals as a math student. So, mathematical minds, we set you off!

This single-volume reference is designed for readers and researchers investigating national and international aspects of mathematics education at the elementary, secondary, and post-secondary levels. It contains more than 400 entries, arranged alphabetically by headings of greatest pertinence to mathematics education. The scope is comprehensive, encompassing all major areas of mathematics education, including assessment, content and instructional procedures, curriculum, enrichment, international comparisons, and psychology of learning and instruction.

Henry O. Pollak Chairman of the International Program Committee Bell Laboratories Murray Hill, New Jersey, USA The Fourth International Congress on Mathematics Education was held in Berkeley, California, USA, August 10-16, 1980. Previous Congresses were held in Lyons in 1969, Exeter in 1972, and Karlsruhe in 1976. Attendance at Berkeley was about 1800 full and 500 associate members from about 90 countries; at least half of these come from outside of North America. About 450 persons participated in the program either as speakers or as presiders; approximately 40 percent of these came from the U.S. or Canada. There were four plenary addresses; they were delivered by Hans Freudenthal on major problems of mathematics education, Hermina Sinclair on the relationship between the learning of language and of mathematics, Seymour Papert on the computer as carrier of mathematical culture, and Hua Loo-Keng on popularising and applying mathematical methods. Gearge Polya was the honorary president of the Congress; illness prevented his planned attendence but he sent a brief presentation entitled, "Mathematics Improves the Mind". There was a full program of speakers, panelists, debates, miniconferences, and meetings of working and study groups. In addition, 18 major projects from around the world were invited to make presentations, and various groups representing special areas of concern had the opportunity to meet and to plan their future activities.